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Math Help - Describe A + B

  1. #1
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    Describe A + B

    Hello. I don't know how to do this
    A = { (x_1,x_2): x_1=0, 0 \leq x_2 \leq 1}
    B = { (x_1,x_2): x_2=2, 0 \leq x_1 \leq 1}

    Describe A+B and A-B.

    Thank you.
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  2. #2
    Super Member TheChaz's Avatar
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    Re: Describe A + B

    Well, these are line segments...

    Do you know what "+" and "-" mean in this context?
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  3. #3
    MHF Contributor alexmahone's Avatar
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    Re: Describe A + B

    Quote Originally Posted by TheChaz View Post
    Well, these are line segments...
    They look like coordinates to me.

    Edit: I see what you mean. But + and - seem to me to be simple addition and subtraction of real coordinates.
    Last edited by alexmahone; October 17th 2011 at 09:16 AM.
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  4. #4
    Super Member TheChaz's Avatar
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    Re: Describe A + B

    Quote Originally Posted by alexmahone View Post
    They look like coordinates to me.
    Indeed, the elements of A and B are coordinates, but isn't the entire set A (B) a line segment/interval of R^2?

    Since A and B aren't real numbers... ???
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  5. #5
    MHF Contributor alexmahone's Avatar
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    Re: Describe A + B

    Quote Originally Posted by Lolyta View Post
    Hello. I don't know how to do this
    A = { (x_1,x_2): x_1=0, 0 \leq x_2 \leq 1}
    B = { (x_1,x_2): x_2=2, 0 \leq x_1 \leq 1}

    Describe A+B and A-B.

    Thank you.
    A + B = { (x_1,x_2): 0 \leq x_1 \leq 1, 2 \leq x_2 \leq 3}
    A - B = { (x_1,x_2): -1 \leq x_1 \leq 0, -2 \leq x_2 \leq -1}
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  6. #6
    MHF Contributor alexmahone's Avatar
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    Re: Describe A + B

    Quote Originally Posted by TheChaz View Post
    Indeed, the elements of A and B are coordinates, but isn't the entire set A (B) a line segment/interval of R^2?

    Since A and B aren't real numbers... ???
    Sorry...
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  7. #7
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    Re: Describe A + B

    Quote Originally Posted by alexmahone View Post
    A + B = { (x_1,x_2): 0 \leq x_1 \leq 1, 2 \leq x_2 \leq 3}
    A - B = { (x_1,x_2): -1 \leq x_1 \leq 0, -2 \leq x_2 \leq -1}
    Thanks a lot for answering but could you explain how you did it?
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  8. #8
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    Re: Describe A + B

    Quote Originally Posted by Lolyta View Post
    Thanks a lot for answering but could you explain how you did it?
    We cannot help until you define what each of A+B~\&~A-B means.
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  9. #9
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    Re: Describe A + B

    Quote Originally Posted by Plato View Post
    We cannot help until you define what each of A+B~\&~A-B means.
    Well, A+B ={ z: z = a+b : a\in{A}; b\in{B}}.
    A-B ={ z: z = a-b : a\in{A}; b\in{B}}.
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  10. #10
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    Re: Describe A + B

    Quote Originally Posted by Lolyta View Post
    Hello. I don't know how to do this
    A = { (x_1,x_2): x_1=0, 0 \leq x_2 \leq 1}
    B = { (x_1,x_2): x_2=2, 0 \leq x_1 \leq 1}
    Describe A+B and A-B.
    So it is coordinate operations.
    Rewrite the B set to make the answer clearer.
    A = { (x_1,x_2): x_1=0, 0 \leq x_2 \leq 1}
    B = \{(x_1,x_2):0 \leq x_1 \leq 1, x_2=2\}

    Now
    A+B=\{x_1,x_2): 0\le x_1\le 1, 2 \leq x_2 \leq 1\}

    A-B=\{x_1,x_2): -1\le x_1\le 0, -2 \leq x_2 \leq -1\}
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  11. #11
    Super Member TheChaz's Avatar
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    Re: Describe A + B

    Then here's your answer.

    Quote Originally Posted by alexmahone View Post
    A + B = { (x_1,x_2): 0 \leq x_1 \leq 1, 2 \leq x_2 \leq 3}
    A - B = { (x_1,x_2): -1 \leq x_1 \leq 0, -2 \leq x_2 \leq -1}
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  12. #12
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    Re: Describe A + B

    Thanks a lot to everyone
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